1 citations · 1 across the 2 of their papers we have counts for
4 papers
Abelian Repetition Threshold Revisited
Elena A. Petrova, Arseny M. Shur
Abelian repetition threshold ART(k) is the number separating fractional Abelian powers which are avoidable and unavoidable over the k-letter alphabet. The exact values of ART(k) ar…
Branching Frequency and Markov Entropy of Repetition-Free Languages
Elena A. Petrova, Arseny M. Shur
We define a new quantitative measure for an arbitrary factorial language: the entropy of a random walk in the prefix tree associated with the language; we call it Markov entropy. W…
Transition Property For Cube-Free Words
Elena A. Petrova, Arseny M. Shur
We study cube-free words over arbitrary non-unary finite alphabets and prove the following structural property: for every pair of -ary cube-free words, if can be inf…
Constructing Premaximal Binary Cube-free Words of Any Level
Elena A. Petrova, Arseny M. Shur
We study the structure of the language of binary cube-free words. Namely, we are interested in the cube-free words that cannot be infinitely extended preserving cube-freeness. We s…